Reducing power control errors in wireless communication system

ABSTRACT

The present invention provides a method for predicting channel power fading in a wireless communications system. This prediction method estimates the channel power fading via oversampling of the received and transmitted powers. The prediction method is then combined with several proposed structures for closed loop power control. The resulting structures result in improved performance in wireless communications systems.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit under 35 U.S.C. §119(e) of thefollowing and commonly-assigned U.S. Provisional Patent Application Ser.No. 60/325,350, entitled “CLOSED LOOP POWER CONTROL TECHNIQUES INWIRELESS SYSTEMS,” filed on Sep. 27, 2001, by Mansour A. Aldajani andAli H. Sayed, which application is incorporated by reference herein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

This invention was made with Government support under Grant Nos.9732376, and 9820765. awarded by the National Science Foundation. TheGovernment has certain rights in this invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to wireless communications systems, and moreparticularly, to closed loop power control techniques for use inwireless communications systems.

2. Description of the Related Art

(Note: This application references a number of different publications asindicated throughout the specification by reference numbers enclosed inbrackets, e.g., [x]. A list of these different publications orderedaccording to these reference numbers can be found below in Section X ofthe specification. Each of these publications is incorporated byreference herein.)

Power control is often necessary in wireless communications systems. Forexample, a DS-CDMA (direct sequence—code division multiple access)wireless communications systems must implement power control, becauseall users share the same bandwidth to transmit data and interferenceamong users often occurs. Generally, the signal received by a basestation (BS) from a nearby mobile station (MS) will dominate thatreceived from a far MS.

The objective of power control is to control the transmission power ofthe MS such that the average received power from each MS is constant.Power control reduces inter-user interference by overcoming the near-fareffect and results in capacity increase of the overall CDMA system.Power control also combats the Rayleigh fading channel effect on thetransmitted signal by compensating for the fast fading of the wirelesschannel. Finally, power control minimizes the power consumption of theMS.

Power control can be classified into two main categories, namely, openloop and closed loop power control. In Open Loop Power Control (OLPC),the MS measures the quality of the signal received from the BS andadjusts its transmission power accordingly. In Closed Loop Power Control(CLPC), the BS measures the fading effects in the signal received fromeach MS, and then commands each MS to increase or decrease its poweraccordingly.

Notwithstanding these accomplishments, there remains a need in the artfor improved methods of power control.

SUMMARY OF THE INVENTION

The present invention analyzes a conventional closed loop control (CLPC)and derives an expression for the power control error in terms of thechannel fading. The expression suggests methods for reducing the errorvariance. This is achieved by using a prediction technique forestimating the channel power fading via oversampling of the received andtransmitted powers. The prediction module is then combined with severalproposed schemes for closed loop power control. The resultingarchitectures are shown to result in improved performance in extensivesimulations.

The contributions of this work can be summarized as follows:

1. The classical closed loop power control used in IS-95 CDMA Wirelesssystems is analyzed using a distinctive approach.

2. A distinctive method suitable for predicting the channel power fadingin wireless systems is developed.

3. Seven new algorithms for closed loop power control are developed andanalyzed.

The algorithms developed in this invention can be used in the powercontrol of next generation wireless and cellular systems.

A general embodiment of the present invention provides for power controlin a wireless communications system, comprising: (a) receiving a signalfrom a remote transmitter; (b) using a prediction technique forestimating channel power fading in the received signal by oversamplingthe received signal; (c) comparing the channel power fading with areference point; and (d) based on the comparison, transmitting a commandto the remote transmitter to alter the signal's power accordingly. Theusing step comprises predicting the channel power fading based onoversampling of the received signal's power variations. The predictingstep comprises using an adaptive predictor for estimating the channelpower fading of the received signal one-step ahead. The commandcomprises an estimate of what the signal's power should be for a nextperiod of time, or a power control error resulting from a differencebetween a desired power level and the received signal's power, whereinthe power control error is a function of a variation in the channelpower fading and a quantization noise of a sign function.

A first embodiment of the present invention provides a Predictive RatioClosed Loop Power Control (PR-CLPC) algorithm, comprising: (a) measuringa received power from a mobile station at a base station; (b) estimatinga channel power fading from a previous transmission power; (c)generating a predicted channel power fading; (d) multiplying thereceived power by a ratio of the predicted channel power fading dividedby the estimated channel power fading to generate a result; (e)comparing the result with a desired power level to determine a powercommand for the mobile station; and (f) transmitting the power commandto the mobile station, wherein the mobile station increments ordecrements its transmission power by a step change in response to thepower command.

A second embodiment of the present invention provides an AdaptivePredictive Ratio—Closed Loop Power Control (APR-CLPC) algorithm,comprising: (a) measuring a received power from a mobile station at abase station; (b) estimating a channel power fading from a previoustransmission power; (c) generating a predicted channel power fading; (d)multiplying the received power by a ratio of the predicted channel powerfading divided by the estimated channel power fading to generate aresult; (e) comparing the result with a desired power level to determinea power command for the mobile station; and (f) transmitting the powercommand to the mobile station, wherein the mobile station computes asignal from the power command and previously-received power commands,computes a term from the signal, computes a step change from the termand increments or decrements its transmission power by the step change.

A third embodiment of the present invention provides a DirectInverse—Closed Loop Power Control (DI-CLPC) algorithm, comprising: (a)measuring a received power from a mobile station at a base station; (b)estimating a channel power fading from a previous transmission power;(c) generating a predicted channel power fading; (d) generating anestimated transmission power from a ratio of the desired power leveldivided by the predicted channel power fading; (e) encoding theestimated transmission power to generate encoded data; and (f)transmitting the encoded data to the mobile station, wherein the mobilestation decodes the encoded data to obtain the estimated transmissionpower and sets its transmission power to the estimated transmissionpower.

A fourth embodiment of the present invention provides an Adaptive DirectInverse—Closed Loop Power Control (ADI-CLPC) algorithm, comprising: (a)measuring a received power from a mobile station at a base station; (b)estimating a channel power fading from a previous transmission power;(c) generating a predicted channel power fading; (d) generating anestimated transmission power from a ratio of the desired power leveldivided by the predicted channel power fading; (e) encoding theestimated transmission power to generate coded data; and (f)transmitting the coded data to the mobile station, wherein the mobilestation decodes the coded data to obtain the estimated transmissionpower and sets its transmission power to the estimated transmissionpower.

A fifth embodiment of the present invention provides an InverseEstimation—Closed Loop Power Control (IE-CLPC) algorithm, comprising:(a) measuring a receive power from a mobile station at a base station;(b) performing a 1-tap equalization using the measured receive power asan input and a previous transmission power as a reference; (c)multiplying a tap value from the 1-tap equalization by a desired powerlevel to generate an estimated transmission power; (d) encoding theestimated transmission power to generate coded data; and (e)transmitting the coded data to the mobile station, wherein the mobilestation decodes the coded data to obtain the estimated transmissionpower and sets its transmission power to the estimated transmissionpower.

A sixth embodiment of the present invention provides an OptimalPredictive—Closed Loop Power Control (OP-CLPC) algorithm, comprising:(a) measuring a received power from a mobile station at a base station;(b) estimating a channel power fading from a previous transmissionpower; (c) generating a predicted channel power fading; (d) multiplyingthe received power by a ratio of the predicted channel power fadingdivided by the estimated channel power fading to generate a firstresult; (e) comparing the first result with a desired power level todetermine a difference; (f) multiplying the difference by the estimatedchannel power fading to generate a second result; (f) multiplying thesecond result by a step size to generate an estimated transmissionpower; (g) encoding the estimated transmission power to generate codeddata; and (h) transmitting the coded data to the mobile station, whereinthe mobile station decodes the coded data to obtain the estimatedtransmission power and sets its transmission power to the estimatedtransmission power.

A seventh embodiment of the present invention provides an ErrorCoding—Closed Loop Power Control (EC-CLPC) algorithm, comprising: (a)measuring a received power from a mobile station at a base station; (b)comparing the received power with a desired power level to generate adifference signal; (g) encoding the difference signal to generate acoded signal; and (h) transmitting the coded signal to the mobilestation, wherein the mobile station decodes the coded signal to obtainthe difference signal and then increments or decrements its transmissionpower using the difference signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings in which like reference numbers representcorresponding parts throughout:

FIG. 1 illustrates the structure of a conventional closed loop powercontrol;

FIG. 2 illustrates the structure of a linear delta modulator;

FIG. 3 illustrates the structure of a conventional closed loop powercontrol;

FIG. 4 illustrates an equivalent structure for conventional closed looppower control;

FIG. 5 is a graph showing the performance of a conventional CLPC versusα for different Doppler frequencies;

FIG. 6 is a graph showing the comparison between the analytical powererror variances of equations (31) (Model 1) and (33) (Model 2) with thesimulation results;

FIG. 7 illustrates the structure used for power fading prediction;

FIG. 8 is a graph showing the time response of the channel attenuationand its prediction for a Rayleigh fading channel;

FIG. 9 is a graph showing the prediction error over time for a Rayleighfading channel with f_(D)=50 Hz and with U=1;

FIG. 10 is a graph showing the effect of the step-size μ on predictionMSE for different Doppler frequencies;

FIG. 11 is a graph showing the prediction MSE as a function of theoversampling factor U for different Doppler frequencies;

FIG. 12 is a block diagram of a Predictive Ratio Closed Loop PowerControl (PR-CLPC);

FIG. 13 illustrates the structure used for evaluation of the predictiveratio, wherein the prediction scheme is the one of FIG. 6;

FIG. 14 is a block diagram of a Direct Inverse Closed Loop Power Control(DI-CLPC);

FIG. 15 is a block diagram of a coding scheme used in the Direct InverseCLPC;

FIG. 16 is a block diagram of a coding scheme used in the AdaptiveDirect Inverse CLPC;

FIG. 17 is a block diagram of a Inverse Estimation Closed Loop PowerControl (IE-CLPC);

FIG. 18 is a block diagram of an Optimal Predictive Closed Loop PowerControl (OP-CLPC);

FIG. 19 is a block diagram of an Error Coding Closed Loop Power Control(EC-CLPC);

FIG. 20 is a graph showing the effect of choosing μ on PCE for thePR-CLPC using α=1.3;

FIG. 21 is a graph showing the effect of choosing α on PCE for thePR-CLPC;

FIG. 22 is a graph showing the power errors for the APR-CLPC algorithmfor two values of the adaptation constant C;

FIG. 23 is a graph showing a typical response for the exponent termα_(c)(n) of the adaptive DI-CLPC algorithm over time for a Rayleighfading channel with f_(D)=85 Hz;

FIG. 24 is a graph showing the performance of the developed algorithmscompared to conventional CLPC and a current adaptive CLPC scheme;

FIG. 25 is a graph showing the coding SNR versus power control errorstandard deviation for IE-CLPC with f_(D)=[10,20,50] Hz;

FIG. 26 is a graph showing the coding SNR versus power control errorstandard deviation for IE-CLPC with f_(D)=[85,100,150] Hz;

FIG. 27 is a graph showing the coding SNR versus power control errorstandard deviation for OP-CLPC with f_(D)=[10,20,50] Hz;

FIG. 28 is a graph showing the coding SNR versus power control errorstandard deviation for OP-CLPC with f_(D)=[85,100,150] Hz;

FIG. 29 is a graph showing the coding SNR versus power control errorstandard deviation for EC-CLPC with f_(D)=[10,20,50] Hz; and

FIG. 30 is a graph showing the coding SNR versus power control errorstandard deviation for EC-CLPC with f_(D)=[85,100,150] Hz.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, reference is made to the accompanyingdrawings which form a part hereof, and which is shown, by way ofillustration, several embodiments of the present invention. It isunderstood that other embodiments may be utilized and structural changesmay be made without departing from the scope of the present invention.

I. Introduction

The requirement of Power Control (PC) in the uplink DS-CDMA system is acritical limitation [1]. Power control is needed in CDMA systems becauseall users share the same bandwidth to transmit data and thus inter-userinterference will occur. The signal received by the BS from a near MSwill dominate that received from a far MS. This phenomenon is referredto as near-far effect.

The objective of power control is to control the transmission power ofeach MS such that the average received power from each MS is constant.Some advantages of power control can be summarized as follows:

1. Power control reduces inter-user interference by overcoming thenear-far effect, which results in capacity increase of the overall CDMAsystem.

2. Power control combats the Rayleigh fading channel effect on thetransmitted signal by compensating for the fast fading of the wirelesschannel. This reduces the required signal-to-noise ratio, E_(b)/N_(o).In perfect power control conditions, power control turns a fadingchannel into an AWGN (additive white Gaussian noise) channel [1].

3. Power control minimizes the power consumption of the MS's. Instead ofusing a fixed maximum power by the MS, it will now use an adaptivetransmission power based on the power control requirements.

Power control can be classified into two main categories, namely, openloop and closed loop power control. In the following, we give a briefdescription of each category.

A. Open Loop Power Control

In Open Loop Power Control (OLPC), the MS measures the quality of thesignal received from the BS and adjusts its transmission poweraccordingly. Since the uplink and downlink channel fading effects arenot strongly correlated, the performance of OLPC is limited. OLPC isusually useful when dealing with slow shadow fading and only reaches thepower requirements on average [1]. Shadow fading is a medium-scalevariation in the power of the received signal, which occurs when the MSmoves behind obstructions such as trees and foliage.

B. Closed Loop Power Control

Closed loop power control (CLPC) is a more effective way of dealing withpower control requirements. In this case, the BS measures the fadingeffects in the signal received from each MS. The received power ismeasured usually by averaging multipe samples of the received sequence,i.e.,

$\begin{matrix}{{P_{r}(n)} = {\frac{1}{T_{p}}{\int_{{({n - 1})}T_{p}}^{{nT}_{p}}{{y^{2}(t)}\ {\mathbb{d}t}}}}} & (1)\end{matrix}$

where T_(p) is the power bit period and y(t) is the received signal atthe BS. The BS then compares the received power with a reference point.Based on this comparison, the BS transmits a one-bit signal, known asthe power bit, to each MS commanding it to increase or decrease itspower by a fixed amount, e.g., 1 dB, 0.5 dB, or 0.25 dB. The power bitrate is 800 Hz in IS-95 standards and 1500 Hz in 3G WCDMA standards.FIG. 1 shows a block diagram of this conventional CLPC scheme, includingpower adapter 100, uplink Tx+Channel+Rx block 102, Power, BER (bit errorrate) and SNR (signal to noise ratio) measurement block 104, summingjunction 106, single bit quantizer 108 and integrator 110. In thedownlink channel, power control is not required since all signals to thedifferent MS's are initiated from the same source.

C. Limitations of Conventional Closed Loop Power Control

FIGS. 2A and 2B illustrate the basic structure a linear delta modulator.FIG. 2A includes a summing junction 200, single bit quantizer 202,integrator 204, and delay 206. FIG. 2B includes a summing junction 208,summing junction 210, integrator 212, and delay 214.

By comparing FIG. 1 and the linear delta modulator shown in FIGS. 2A and2B, it can be seen that a conventional CLPC behaves similarly to a deltamodulator (DM). Both feedback systems implement two similar operations:sign-of-error and integration. This explains the slow trackingperformance exhibited by conventional CLPC in the presence of fast anddeep fading of the wireless channel. In addition, CLPC creates a noisyresponse when the fading is smooth or minimal.

In the literature, there have been two main methods used to improve theperformance of the conventional CLPC, namely, adaptive step-size andpredictive power control. In adaptive step-size power control, thestep-size of the power error quantizer is adapted in a way to cope withthe quickly changing and deep channel fading effects. Examples of suchschemes can be found in [3], [4], [5], [6]. Predictive power control, onthe other hand, is based on predicting the channel attenuation one stepahead [7], [8], [10]. The predicted value is then used in calculatingthe predicted received power.

In this work, we quantify, mathematically, the performance of theconventional CLPC system. In particular, we shall derive an expressionfor the power control error (PCE). This expression will unveil the mainfactors contributing to the limited performance of the conventional CLPCscheme. Later, we shall use these insights to develop new algorithms toovercome these limiting factors and obtain improved power controlperformance.

II. Analysis of Conventional CLPC

A. Power Channel Model

Let us first describe a model for the wireless channel. In this model,we consider the effect of the uplink channel on the power envelope ofthe received signal. We assume a multi-path channel with Rayleigh fadingreflections that are optimally combined using a RAKE receiver with Mfingers. The discrete-time received power P_(r)(n) at the BS can beexpressed as [9], [10]:

$\begin{matrix}{{P_{r}(n)} = {\frac{1}{T_{p}}{\int_{{({n - 1})}T_{p}}^{{nT}_{p}}{{P_{t}(t)}{Q(t)}\ {\mathbb{d}t}}}}} & (2)\end{matrix}$

where T_(p) is the power control period P_(t)(t), is the transmissionpower, and Q(t) is the power gain of the channel. This gain contains alleffects of the multipath reflections on the signal power. In [9], thegain Q(t) is given by

$\begin{matrix}{{Q(t)} = {\sum\limits_{p = 0}^{L - 1}\;{a_{p}^{2}(t)}}} & (3)\end{matrix}$

where a_(p) is the tap weight coefficient relative to the p th finger ofthe RAKE receiver. In (3) it is assumed that the channel AWGN is“cancelled” by the receiver and that any slow shadow fading by thechannel is accounted for by the open loop power control. Therefore, theAWGN is removed from the channel modeling.

The transmission power P_(t)(t) is kept unchanged during a power controlperiod, so that

$\begin{matrix}{{{P_{r}(n)} = {{P_{t}\left( {n - 1} \right)}\left\lbrack {\frac{1}{T_{p}}{\int_{{({n - 1})}T_{p}}^{{nT}_{p}}{{Q(t)}\ {\mathbb{d}t}}}} \right\rbrack}}{{Let}\mspace{14mu}{us}\mspace{14mu}{denote}}} & (4) \\{{\phi(n)}\underset{\underset{\_}{\_}}{\Delta}\frac{1}{T_{p}}{\int_{{({n - 1})}T_{p}}^{{nT}_{p}}{{Q(t)}\ {\mathbb{d}t}}}} & (5)\end{matrix}$

Then the received power is modeled byP _(r)(n)=φ(n)P _(t)(n−1)  (6)

We shall further assume that the power bit is transmitted from the BS tothe MS through the down-link channel with zero BER (bit error rate).

B. Equivalent Model for Conventional CLPCP

FIG. 3 shows a more detailed block diagram of the conventional CLPC,wherein the BS includes a summing junction 300, single bit quantizer302, and power measurement block 304, and the MS includes exponentialterm block 306, multiplier 308, delays 310 and 312, zero-order hold 314,and selectable power adapter 316. The channel between the BS and MS actsas a multiplier 318 between the signal transmitted by the MS and thechannel power fading φ(t).

As shown in FIG. 3, the transmission power P_(t)(t) used by the MS isattenuated by the channel fading φ(t). At the BS, the received powerP_(r)(n) is measured and it is then compared to a desired fixed powerlevel P_(d). The error e_(a)(n) is given bye _(a)(n)=P _(d) −P _(r)(n)  (7)

Equivalently, using (6), we can writee _(a)(n)=P _(d)−φ(n)P _(t)(n−1)  (8)

The power error e_(a)(n) is quantized using a one-bit quantizer toproduce the power command bit (PCB) denoted as b(n) scaled by half thestep-size of the quantizer Δ, i.e.,

$\begin{matrix}{{b(n)} = {\frac{\Delta}{2}{{sign}\left\lbrack {e_{a}(n)} \right\rbrack}}} & (9)\end{matrix}$

This PCB is transmitted to the MS. The MS then increments or decrementsits transmission power by a fixed amount (in dB). The process ismathematically expressed asP _(t)(n)=α^(b(n)) P _(t)(n−1)  (10)where α is a constant (usually 1<α<3). In other words, P_(t)(n) isincremented or decremented by ψdB whereψ=10 log₁₀α  (11)

Equivalently, for ψdB change in P_(t)(n), α should be 10^(ψ/10).

Let us now take the logarithm of both sides of equation (10):log_(α) P _(t)(n)=b(n)+log_(α) P _(t)(n−1)  (12)

Using (8) and (9) we can write

$\begin{matrix}{{b(n)} = {\frac{\Delta}{2}{{sign}\left\lbrack {P_{d} - {{\phi(n)}{P_{t}\left( {n - 1} \right)}}} \right\rbrack}}} & (13)\end{matrix}$

Now, since the logarithm is an increasing function, we can rewrite thisequation as

$\begin{matrix}{{{b(n)} = {\frac{\Delta}{2}{{sign}\left\lbrack {{\log_{\alpha}P_{d}} - {\log_{\alpha}\left( {{\phi(n)}{P_{t}\left( {n - 1} \right)}} \right)}} \right\rbrack}}}{{Equivalently},}} & (14) \\{{{b(n)} = {\frac{\Delta}{2}{{sign}\left\lbrack {{\log_{\alpha}P_{d}} - {\log_{\alpha}{\phi(n)}} - {\log_{\alpha}{P_{t}\left( {n - 1} \right)}}} \right\rbrack}}}{{Therefore},}} & (15) \\{{b(n)} = {\frac{\Delta}{2}{{sign}\left\lbrack {{\log_{\alpha}\frac{P_{d}}{\phi(n)}} - {\log_{\alpha}{P_{t}\left( {n - 1} \right)}}} \right\rbrack}}} & (16)\end{matrix}$

Substituting this expression into (12), we get

$\begin{matrix}{{\log_{\alpha}{P_{t}(n)}} = {{\log_{\alpha}{P_{t}\left( {n - 1} \right)}} + {\frac{\Delta}{2}{{sign}\left\lbrack {{\log_{\alpha}\frac{P_{d}}{\phi(n)}} - {\log_{\alpha}{P_{t}\left( {n - 1} \right)}}} \right\rbrack}}}} & (17)\end{matrix}$

This expression shows that in the logarithmic scale, the relationbetween {P_(d), P_(t)(n)} amounts to a delta modulation scheme withinput

$\log_{\alpha}\frac{P_{d}}{\phi(n)}$and output log_(α)P_(t)(n), as shown in FIG. 4.

FIG. 4 illustrates an equivalent structure for a conventional CLPC,including a logarithm function 400, delta modulator 402, and exponentialfunction 404. This function of this structure is denoted as K(n).

The logarithmic function is added before the delta modulator, while theexponential function is added after the delta modulator to get P_(t)(n).

In other words, the result (17) shows that the conventional CLPC modelof FIG. 3 is actually a companded delta modulator with input

$\frac{P_{d}}{\phi(n)}$and output P_(t)(n). That is, the CLPC attempts to make the transmissionpower P_(t)(n) track the quantity

$\frac{P_{d}}{\phi(n)}$using a companded delta modulator.

C. Power Control Error

Delta modulation is actually the simplest tracking system used in codingand data conversion. It can be shown (e.g., as in [11], [12], [13]) thatP_(t)(n) is related to log_(α)

$\log_{\alpha}\frac{P_{d}}{\phi(n)}$via the model

$\begin{matrix}{{P_{t}(n)} = {{\alpha^{\log_{\alpha}\frac{P_{d}}{\phi{(n)}}}{K(n)}} = {\frac{P_{d}}{\phi(n)}{K(n)}}}} & (18)\end{matrix}$where K(n) is a random variable that is defined byK(n)=α^(e) ^(d) ^((n))  (19)and e_(d)(n) is a uniform quantization noise in

$\left\lbrack {{- \frac{\Delta}{2}},\frac{\Delta}{2}} \right\rbrack,$where Δ is the step-size of the one-bit quantizer inside the deltamodulator. If we substitute (18) into (6), we find that

$\begin{matrix}{{P_{r}(n)} = {\frac{\phi\;(n)}{\phi\;\left( {n - 1} \right)}{P_{d}\left( {n - 1} \right)}\; K\;\left( {n - 1} \right)}} & (20)\end{matrix}$

For the sake of compactness, let us introduce the notation(.)

10 log₁₀(.)  (21)

Therefore,P _(r)(n)= φ(n)− φ(n−1)+ P _(d) + K (n−1)  (22)

Since K(n)=α^(e) ^(d) ^((n)) and α=10 log₁₀α=ψ, thenK (n)=ψe _(d)(n)  (23)

By substituting (23) into (22), we arrive at the following expressionfor the received power:P _(r)(n)= φ(n)− φ(n−1)+ P _(d) +ψe _(d)(n−1)  (24)

Let us define the power error in dB as

$\begin{matrix}{{e(n)}\overset{\Delta}{=}{{{\overset{\_}{P_{r}}(n)} - \overset{\_}{P_{d}}} = {10\;\log_{10}\frac{P_{r}(n)}{P_{d}}}}} & (25)\end{matrix}$where this error is just another way of measuring the difference betweenP_(r)(n) and P_(d). It employs a logarithmic scale, while the earliererror e_(a)(n), defined in FIG. 3, employs a linear scale.

Then, from (24),e(n)= φ(n)− φ(n−1)+ψe _(d)(n−1)  (26)

This expression shows that the power error, e(n), is determined by twofactors:

1. The variance in the channel power fading, φ(n)− φ(n−1).

2. The quantization noise e_(d)(n).

Observe that the linear relation (26) is valid in the logarithmic scale.

In the following two subsections, we proceed to derive expressions forthe mean and variance of e(n). To do so, we make the followingassumptions:

A.1. e_(d)(n) is a uniformly distributed random variable in

$\left\lbrack {{- \frac{\Delta}{2}},\frac{\Delta}{2}} \right\rbrack.$

A.2. All random processes are stationary and independent of each other.

D. Mean and Variance Analysis

Let us take the expected value of both sides of (26), i.e.,E{e(n)}=E{ φ(n)}−E{ φ(n−1)}+ψE{e _(d)(n−1)}  (27)

Based on the stationarity assumption, at steady state, we writeE{ φ(n)}=E{ φ(n−1)}

E _(φ)

Also, since E{e_(d)(n−1)}=0, we conclude thatE _(e)

E{e(n)}=0  (28)

To evaluate the variance of e(n), let us square both sides of (26) asfollows:e ²(n)=( φ(n)− φ(n−1))²+2( φ(n)− φ(n−1))ψe _(d)(n−1)+ψ² e _(d)²(n−1)  (29)

Using the uncorrelatedness assumption A.1:E{( φ(n)− φ(n−1))ψe _(d)(n−1)}=0  (30)we find thatE{e ²(n)}=E{( 100 (n)− φ(n−1))² }+ψ ² E{e _(d) ²(n−1)}  (31)

When the uniformity assumption A.2 on the quantization noise e_(d)(n) isreasonable, we further have

$\begin{matrix}{{E\left\{ {e_{d}^{2}\left( {n - 1} \right)} \right\}} = {{\int_{\frac{\Delta}{2}}^{\frac{\Delta}{2}}{\frac{1}{\Delta}x^{2}{\mathbb{d}x}}} = \frac{\Delta^{2}}{12}}} & (32)\end{matrix}$so that the power error variance can be expressed as

$\begin{matrix}{{E\left\{ {e^{2}(n)} \right\}} = {{E\left\{ \left( {{\overset{\_}{\phi}\;(n)} - {\overset{\_}{\phi}\;\left( {n - 1} \right)}} \right)^{2} \right\}} + {\psi^{2}\frac{\Delta^{2}}{12}}}} & (33)\end{matrix}$

Lemma 1 (Power Control Error) For the CLPC scheme of FIG. 3, the powercontrol error e(n)≡ P _(r)(n)− P _(d) is zero mean while its variance isgiven by (31). When the uniformity assumption on the quantization noiseis reasonable, the error variance is reduced to (33).

E. Effect of the Choice of α

Referring to the companded delta modulator structure of FIG. 4, we seethat there are some restrictions on the choice of the positive quantityα.

Clearly, α cannot be less than unity since it will then expand (insteadof compress) the input to the delta modulator. This will result in slopeoverload, in which the delta modulator cannot cope with the largevariations in the input. Furthermore, α cannot be unity since thischoice has no meaning and will make the system functionless(P_(t)(n)=P_(t)(n−1)). The larger than unity α is, the less slopeoverload there is in the system (which makes the tracking easier for thedelta modulator). However, from (26), increasing α will increase thepower tracking error thus putting a limitation on how large can α be. Insummary, the best choice for α should be the one that comprises theincrease in compression to the delta modulator input and the decrease inthe power tracking error.

To see the effect of α on the power control error, we choose a certainDoppler frequency f_(D), which is the width of the Doppler powerspectrum of the wireless channel. The Doppler frequency and the delayspread of the channel are reciprocally related.

This information is then used to generate the corresponding multipathgains. The power fading φ(n) is then computed from (3) and (5). We alsochoose a value for the exponent term α and we run a simulationimplementing the CLPC of FIG. 3. The standard deviation of the errore(n) is measured. The values of f_(D) and α are then changed and thestandard deviation is measured again. The result is shown in FIG. 5,which illustrates the performance of conventional CLPC versus α fordifferent Doppler frequencies. This figure shows that the optimal choiceof a α lies in the interval from 1 to 2. The heavy solid curve indicatesthe optimal path of α as a function of f_(D).

In addition, considering the power error variance expression (31), astrong matching between analytical and simulation results was observed.This expression assumes however that the second moment of thequantization error e_(d)(n) can be well estimated. The second expressionfor the error variance shown in (33) is more specific to the case wherethe uniformity assumption of the quantization error is reasonable byproper choice of α (the uniformity assumption is dependent on the amountof slope overload of the delta modulator, which is controlled by α).

FIG. 6 shows a comparison between the simulation and analytical resultsof the power control error standard deviation with f_(D)=85 Hz. Thecurve associated with equation (31) shows a strong match to thesimulation results for all 1<α<2. On the other hand, the curveassociated with equation (33) matches simulation results only at largeenough α's, as expected. This supports our conclusion that equation (33)should be used only if the uniformity assumption holds. Otherwise,equation (31) should be used with a more accurate characterization ofe_(d)(n).

III. Oversampled Channel Prediction

In the next section, we shall develop several method for CLPC. Most ofthese methods will require a prediction for the channel power fadingφ(n). In this section, we describe a method for predicting φ(n). Themethod is based on oversampling the received power variations at the BS.Then an adaptive predictor, for example, a NLMS-based(normalized-least-mean-square) filter or any other similar adaptivefitter, is used to estimate the channel fading one-step ahead. For thispurpose, we assume that the BS knows the transmission power P_(t)(n) ofthe MS at each time instant. This assumption is reasonable in CLPC sincethe BS can compute P_(t)(n) from the information sent to the MS.

FIG. 7 shows the structure for implementing the proposed power fadingprediction method, including divider 700, up-sampler block 702, delay704, adaptive filter 706, summing junction 708, finite impulse response(FIR) filter 710, and down-sampler block 712.

In this structure, the measured received power P_(r)(n) is divided byP_(t)(n−1) to get the power channel fading or power attenuation φ(n),i.e.,

$\begin{matrix}{{\phi(n)} = \frac{P_{r}(n)}{P_{t}\;\left( {n - 1} \right)}} & (34)\end{matrix}$

The signal φ(n) is then up-sampled by a factor of U resulting in φ(m),where m refers to the oversampling index. This can be achieved byincreasing the sampling rate of the received power and by assuming thatthe transmission power is constant between two consecutive samples ofP_(t)(n).

The signal φ(m) is then passed through a delay as shown in FIG. 7. Thedelayed samples of φ(m−1) are fed into an adaptive filter of order M.The output of the adaptive filter is compared to φ(m). The comparisonerror is fed back to the adaptive filter for online training. The taps,W_(m), of the adaptive filter extract the correlation between the fadingsamples. The tap values are carried out online and used to adapt thetaps of an FIR (finite impulse response) filter as shown in the figure.The input to this FIR filter is φ(m) and its output is the prediction ofφ(m+1) denoted by φ_(p)(m+1|m). This signal is then down-sampled by thefactor U to produce the required prediction valueφ_(p)(n+1|n)≈φ(n+1)  (35)The NLMS algorithm can be used here to update the weight vector W.

The performance of this predictor is dependent on many factors such asthe filter type, order, and step-size. Furthermore, the oversamplingfactor U plays a significant role in the performance of the predictorsince it increases the correlation between the samples of φ(m).

It should be noticed here that increasing U will introduce noise in themeasured P_(r)(n) resulting in degradation in performance. This usuallysets an upper limit for choosing U. We found through simulations thatU≦5 is an acceptable choice.

FIG. 8 shows an attenuation curve φ(n) resulting from a Rayleigh fadingchannel together with its predicted value φ_(p)(n+1|n).

FIG. 9 shows a plot of the prediction error e_(pr)=φ_(p)(n+1|n)−φ(n+1)over time for a Rayleigh fading channel with f_(D)=50 Hz, U=1, andμ=1.8. The error decays to −40 dB and stays under −30 dB for most of thesimulation time. In FIG. 10, we show the prediction mean square errorE{e_(pr) ²} (MSE) versus the step-size μ. The MSE can be further reducedby increasing the oversampling factor U. In FIG. 11, the MSE is shown asa function of U for different f_(D)'s and for μ=1.2.

IV. New Adaptive Methods for Closed Loop Power Control

We derived an expression for the power control error (PCE) of theconventional IS-95 closed loop power control (CLPC). In particular, weshowed that the power error function, in dB, is given bye(n)

P _(r)(n)− P _(d)= φ(n)− φ(n−1)+ψe _(d)(n−1)  (36)wherein:

P _(r)(n)=10 log₁₀P_(r)(n)=10 log₁₀(φ(n)P_(t)(n−1)): received power atthe BS in dB,

P _(d)=10 log₁₀P_(d): desired power in dB,

φ(n)=10 log₁₀φ(n): power fading caused by the channel in dB,

ψ=10 log₁₀α: increment in transmission power in dB,

P_(t)(n): transmitted power by the MS,

e_(d)(n): quantization error,

ψ=10 log₁₀α: increment in transmission power in dB, and

α: the increment in transmission power in dB.

Expression (36) shows that the sign of the power control error, e(n), isaffected by two factors:

1. The variation in the channel fading power, namely φ(n)− φ(n−1) wherefrom (3)-(5):

$\begin{matrix}{{\phi(n)}\overset{\Delta}{=}{\frac{1}{T_{P}}{\int_{{({n - 1})}_{P}^{T}}^{{nT}_{p}}{\left\lbrack \ {\sum\limits_{P = 0}^{L - 1}\;{a_{P}^{2}(t)}} \right\rbrack{\mathbb{d}t}}}}} & (37)\end{matrix}$

and a_(p)(t) denotes the p th tap of the fading channel at time t.Moreover, T_(p) is the power control period andφ(n)=10 log₁₀φ(n) (dB)

2. The quantization noise, e_(d)(n), that is introduced by the one-bitquantizer of FIG. 3. The noise is generally assumed to be uniformlydistributed in an interval

$\left\lbrack {{- \frac{\Delta}{2}},\frac{\Delta}{2}} \right\rbrack,$where Δ is the step-size of the quantizer.

These facts suggest new strategies for reducing the power control errore(n), and consequently improving the performance of the closed looppower control mechanism. In the following, we propose three strategies.

1. Predictive Power Control: In this scheme, the control law leads toexpression (36) with φ(n−1) replaced by the one-step prediction of φ(n);i.e., φ(n−1) is replaced by φ _(p)(n|n−1). We will see that this can beachieved by introducing a certain ratio block at the BS receiver. Inthis way, we replace the term φ(n−1) in (36) by one that is closer invalue to φ(n). The error can be further reduced by using a variable α(or ψ) depending on the variation in the channel fading.

2. Inverse Power Control: The basic principle here is not to provide theMS with commands to increase or decrease its power according to how farits transmitted power is from the reference level point. Instead, theidea is for the BS to estimate what the transmitted power should be forthe next period of time and to provide this value directly (in codedform) to the MS.

3. Error Coding Power Control: In the conventional scheme of FIG. 3, itis only the sign of the error signale _(a)(n)=P _(d) −P _(r)(n)that is transmitted to the MS. More information about e_(a)(n) can betransmitted to the MS than just its sign. This can be achieved byimplementing a more advanced coding algorithm. The MS will then use thisextra information to improve the performance of the control loop.

V. Predictive Power Control

We begin by discussing the first method of predictive control. Twoalgorithms are proposed in this section.

A. Algorithm 1: Predictive Ratio CLPC (PR-CLPC)

In this algorithm, we end up replacing φ(n−1) by φ _(p)(n|n−1). Theblock diagram of the proposed scheme is shown in FIG. 12, wherein the BSincludes a summing junction 1200, single bit quantizer 1202, powermeasurement block 1204, and a ratio block 1206, and the MS includes anexponential term block 1208, multiplier 1210, delays 1212 and 1214,zero-order hold 1216, and selectable power adapter 1218. The channelbetween the BS and MS acts as a multiplier 1220 between the signaltransmitted by the MS and the channel power fading φ(t).

As shown, the only modification to the conventional CLPC of FIG. 3 isthe introduction of the ratio block

$\frac{\phi_{p}\left( {n + 1} \middle| n \right)}{\phi(n)}.$This will cancel the fading φ(n) caused by the channel and replace it bythe prediction φ_(p)(n+1|n). Everything else is the same as in theconventional CLPC of FIG. 3.

If we follow the same derivation as in Sections II-B and II-C, we canverify that

$\begin{matrix}{{P_{t}(n)} = {\frac{P_{d}}{\phi_{p}\left( {n + 1} \middle| n \right)}{K(n)}}} & (38)\end{matrix}$so that the received power is now given by

$\begin{matrix}{{P_{r}(n)} = {{{\phi(n)}{P_{t}\left( {n - 1} \right)}} = {\frac{\phi(n)}{\phi_{p}\left( n \middle| {n - 1} \right)}{P_{d}\left( {n - 1} \right)}{K\left( {n - 1} \right)}}}} & (39)\end{matrix}$

If we take the logarithm of both sides, as we did in Section II-C, wegetP _(r)(n)= φ(n)− φ _(p)(n|n−1)+ P _(d) + K (n−1)  (40)

In other words,P _(r)(n)= φ(n)− φ _(p)(n|n−1)+ P _(d) +ψe _(d)(n−1)  (41)and, hence, the power error is now given bye(n)= φ(n)− φ _(p)(n|n−1)+ψe _(d)(n−1)  (42)

Notice that the only difference between (36) and (42) is that the termφ(n−1) is replaced by φ _(p)(n|n−1). The power error is now dependent onthe difference [ φ(n)− φ _(p)(n|n−1)] instead of [ φ(n)− φ(n−1)], as isconventional CLPC. Since for reasonable prediction, φ _(p)(n|n−1) isusually closer to φ(n) than φ(n−1), we expect this algorithm to resultin lower PCE. The prediction term φ _(p)(n+1|n) can be evaluated byresorting to the scheme of FIG. 7. In this way, the power measurementand ratio blocks on the left-hand side of FIG. 12 (at BS side) can bemore explicitly detailed as shown in FIG. 13, wherein the received userdata is input to power measurement block 1300, which outputs signalsP_(r)(n) and P_(t)(n−1), which are input to prediction block 1302, whichoutputs signals φ_(p)(n+1|n) and φ(n), which are input to ratio block1304.

We can still evaluate the mean and variance of the power error byfollowing the same procedure and same assumptions as in the conventionalcase of Section II-C. The error mean is given byE{e(n)}=E{ φ(n)}−E{ φ _(p) n|n−1)}+ψE{e _(d)(n−1)}=0  (43)and the error variance isE{e ²(n)}=E{( φ(n)− φ _(p) n|n−1))²}+ψ² E{e _(d) ²(n−1)}  (44)Again, when the uniformity assumption on the quantization noise e_(d)(n)is reasonable, we get

$\begin{matrix}{{E\left\{ {e^{2}(n)} \right\}} = {{E\left\{ \left( {{\overset{\_}{\phi}(n)} - {{\overset{\_}{\phi}}_{p}\left( n \middle| {n - 1} \right)}} \right)^{2} \right\}} + {\psi^{2}\frac{\Delta}{12}}}} & (45)\end{matrix}$

Therefore, the variance of the PCE is now dependent on the second momentE{( φ(n)− φ _(p)(n|n−1))²} and not on E{( φ(n)− φ(n−1))²}, as in theconventional case. Thus, any prediction with acceptable accuracy willimprove the power control error.

The PR-CLPC algorithm is summarized in Table I below:

TABLE I Summary of the Predictive Ratio CLPC (PR-CLPC) algorithmInitialization: Choose the desired received power P_(d). Choose α andevaluate ψ from (11). Choose the prediction parameters: Filter order, μ,and U. For every CLPC time sample n > 0 do: BS: 1. Measure P_(r)(n) fromthe received sequence. 2. Knowing P_(t)(n − 1), estimate φ(n). 3.Evaluate φ_(p)(n + 1|n). 4.${Multiply}\mspace{14mu}{P_{r}(n)}\mspace{14mu}{by}\mspace{14mu}{\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi(n)}.}$5. Compare the result with P_(d):${{if}\mspace{14mu}{P_{r}(n)}\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi(n)}} > P_{d}$then b(n) = 1 else b(n) = −1 end 6. Send b(n) to the MS. MS: 7. Extractb(n) from the received data. 8. If b(n) = 1, then increment P_(t)(n) byψdB else decrement P_(t)(n) by ψdB end.

B. Algorithm 2: Adaptive Predictive Ratio CLPC (APR-CLPC)

This algorithm is an extension to the Predictive Ratio CLPC algorithm.Here, we use an adaptation technique to vary the exponent term α (whichdetermines the value of ψ). The motivation behind this algorithm is thefollowing. When the power fading variations are small, the predictorperforms well. Therefore, we can decrease α to further decrease thepower error of (36). When the variations are large, α is increased toboost the tracking capabilities of the power control loop. Theadaptation scheme used for α isα(n)=α(n−1)+λ(n)C  (46)

where C is a positive constant, usually C<1 (e.g., C=0.2). The signalλ(n) is chosen as follows:

$\begin{matrix}{{\lambda(n)} = \left\{ {\begin{matrix}\begin{matrix}{+ 1} \\{- 1}\end{matrix} \\0\end{matrix}\begin{matrix}\begin{matrix}{if} \\{if}\end{matrix} \\{{otherwise}.}\end{matrix}\begin{matrix}\begin{matrix}{{b(n)} = {{b\left( {n - 1} \right)} = {b\left( {n - 2} \right)}}} \\{{b(n)} \neq {b\left( {n - 1} \right)}}\end{matrix} \\\;\end{matrix}} \right.} & (47)\end{matrix}$

Furthermore, the exponent term α(n) is limited by lower and upperbounds, i.e.,

$\begin{matrix}{{\alpha(n)} = \left\{ {\begin{matrix}\alpha_{\max} \\\alpha_{\max}\end{matrix}\begin{matrix}{if} \\{if}\end{matrix}\begin{matrix}{{\alpha(n)} > \alpha_{\max}} \\{{\alpha(n)} < \alpha_{\min}}\end{matrix}} \right.} & (48)\end{matrix}$

The bounds α_(max) and α_(min) are chosen in the interval (1,3] (e.g.,α_(max)=2.5, α_(min)=1.1).

The step change of P_(t)(n) in dB isψ(n)=10 log₁₀α(n)  (49)

The APR-CLPC algorithm is summarized in Table II below:

TABLE II Summary of the Adaptive Predictive Ratio CLPC (APR-CLPC)algorithm Initialization: Choose the desired received power P_(d).Choose the adaptation parameters: C, α_(max) and α_(mm). Choose theprediction parameters: Filter order, μ, and U. For every CLPC timesample n > 0 do: BS: 1. Measure P_(r)(n) from the received sequence. 2.Knowing P_(t)(n − 1), estimate φ(n). 3. Evaluate φ_(p)(n + 1|n). 4.${Multiply}\mspace{14mu}{P_{r}(n)}\mspace{14mu}{by}\mspace{14mu}{\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi(n)}.}$5. Compare the result with P_(d):${{if}\mspace{14mu}{P_{r}(n)}\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi(n)}} > P_{d}$then b(n) = 1 else b(n) = −1 end 6. Send b(n) to the MS. MS: 7. Extractb(n) from the received data. 8. From b(n − i), i = 0, 1, 2, computeλ(n). 9. From (46) and (49) compute α(n) and ψ(n). 10.  If b(n) = 1,then increment P_(t)(n) by ψ(n)dB else decrement P_(t)(n) by ψ(n)dB end.

VI. Inverse Power Control

We now describe two algorithms for power control that rely on inversecontrol ideas. The basic principle here is not to provide the MS withcommands to increase or decrease its power according to how far itstransmitted power is from the reference level point. Instead, the ideais for the BS to estimate what the transmitted power should be for thenext period of time and to provide this value directly (in coded form)to the MS.

A. Algorithm 1: Direct Inverse CLPC (CI-CLPC) A block diagram of theproposed scheme is shown in FIG. 14, wherein the BS includes a divider1400, encoder 1402, decoder 1404, delay 1406, prediction block 1408, andpower measurement block 1410, and the MS includes a decoder 1412,zero-order hold 1414, and selectable power control 1416. The channelbetween the BS and MS acts as a multiplier 1418 between the signaltransmitted by the MS and the channel power fading φ(t).

In FIG. 14, the power control process works as follows. The BS measuresthe received power P_(r)(n) from the bit stream arriving at its end.Then, the MS transmission power P_(t)(n−1) and P_(r)(n) are fed to theprediction block, which produces φ_(p)(n+1|n) as in FIG. 13. The BSestimates the transmission power that should be used by the MS as

$\begin{matrix}{{{\hat{P}}_{t}(n)} = \frac{P_{d}}{\phi_{d}\left( {n + 1} \middle| n \right)}} & (50)\end{matrix}$

This information is to be transmitted to the MS. Since we are limited bythe power bit rate, {circumflex over (P)}_(t)(n) should be coded to meetthis rate.

The coding scheme used to transmit {circumflex over (P)}_(t)(n) could bethe adaptation part of the ADM described in [12]. This coder exhibitsstrong tracking, good stability, and high dynamic range.

FIG. 15 shows a block diagram of this coding scheme, which includes asumming junction 1500, single bit quantizer 1502, integrator 1504,exponential term block 1506, and delay 1508. The equations describingthe dynamics of the coder are:e _(c)(n)={circumflex over (P)} _(t)(n)−d(n−1), d(0)=d ₀q(n)=sign[e _(c)(n)]w(n)=w(n−1)+q(n), w(0)=0d(n)=α_(c) ^(w(n))  (51)

In this algorithm, the term α_(c) denotes the coding exponent (thesubscript c is added to distinguish it from the α used in the previousalgorithms).

The DI-CLPC algorithm is summarized in Table III below:

TABLE III Summary of the Direct Inverse CLPC (DI-CLPC) algorithmInitialization: Choose the desired received power P_(d). Choose thecoding parameters α_(c) and d(0). Choose the prediction parameters:Filter order, μ, and U. For every CLPC time sample n > 0 do: BS: 1.Measure P_(r)(n) from the received sequence. 2. Knowing P_(t)(n − 1),estimate φ(n). 3. Evaluate φ_(p)(n + 1|n). 4.${{Code}\mspace{14mu}{the}\mspace{14mu}{power}\mspace{14mu}{data}\mspace{14mu}{{\hat{P}}_{t}(n)}} = {\frac{P_{d}}{\phi_{p}\left( {{n + 1}❘n} \right)}.}$5. Send the coded data q(n) to the MS. MS: 6. Extract q(n) from thereceived data. 7. Use q(n) to decode the power data d(n). 8. SetP_(t)(n) = d(n).

B. Algorithm 2: Adaptive Direct Inverse CLPC (ADI-CLPC)

In this algorithm, we modify the coding scheme of the DI-CLPC by usingan adaptive exponent term α_(c), as shown in FIG. 16, which includes asumming junction 1600, single bit quantizer 1602, integrator 1604,exponential term block 1606, and delay 1608. Also included is asub-adaptation block 1610.

The purpose of adapting α_(c) is similar to that in the APR-CLPCalgorithm, namely, to cope with large variations in the channel powerfading. Moreover, the same adaptation technique for α used in APR-CLPCis adopted here, i.e.,α_(c)(n)=α_(c)(n−1)+λ(n)C  (52)where

$\begin{matrix}{{\lambda(n)} = \left\{ {\begin{matrix}\begin{matrix}{{+ 1},} \\{- 1}\end{matrix} \\{0,}\end{matrix},{\begin{matrix}\begin{matrix}{if} \\{if}\end{matrix} \\{otherwise}\end{matrix}\begin{matrix}\begin{matrix}{{q(n)} = {{q\left( {n - 1} \right)}\mspace{14mu}{and}\mspace{14mu}{q\left( {n - 2} \right)}}} \\{{q(n)} \neq {q\left( {n - 1} \right)}}\end{matrix} \\\;\end{matrix}{and}}} \right.} & (53) \\{{\alpha(n)} = \left\{ {\begin{matrix}\alpha_{\max} \\\alpha_{\max}\end{matrix}\begin{matrix}{if} \\{if}\end{matrix}\begin{matrix}{{\alpha(n)} > \alpha_{\max}} \\{{\alpha(n)} < \alpha_{\min}}\end{matrix}} \right.} & (54)\end{matrix}$

with typical values C=0.2, α_(max)=2.5, and α_(min)=1.1 The ADI-CLPCalgorithm is summarized in Table IV below:

TABLE IV Summary of the Adaptive Direct Inverse CLPC (ADI-CLPC)algorithm Initialization: Choose the desired received power P_(d).Choose the prediction parameters: Filter order, μ, and U. Choose theadaptation parameters: C, α_(max) and α_(min). For every CLPC timesample n > 0 do: BS: 1. Measure P_(r)(n) from the received sequence. 2.Knowing P_(t)(n − 1), estimate φ(n). 3. Evaluate φ_(p)(n + 1|n) 4.Compute λ(n) and α_(c)(n) from (52) and (53). 5.${{Use}\mspace{14mu}{\alpha_{c}(n)}\mspace{14mu}{to}\mspace{14mu}{code}\mspace{14mu}{{\hat{P}}_{t}(n)}} = \frac{P_{d}}{\phi_{p}\left( {n + 1} \middle| n \right)}$6. Send the coded data q(n) to the MS. MS: 7. Extract q(n) from thereceived data. 8. Use (52) and (53) to recompute α_(c)(n). 9. Decoded(n) from q(n) and α_(c)(n). 10.  Set P_(t)(n) = d(n).

C. Algorithm 3: Inverse Estimation CLPC (IE-CLPC)

In FIG. 14, the estimate of the transmitted power, {circumflex over(P)}_(t)(n), is obtained by relying on the prediction scheme of FIG. 7.This scheme utilizes P_(r)(n) and P_(t)(n−1), along with upsampling, toevaluate the prediction φ_(p)(n+1|n), which is then used to evaluate{circumflex over (P)}_(t)(n).

Alternatively, one could employ a simplified adaptive structure toestimate

$\frac{1}{\phi\left( {n + 1} \right)}.$More specifically, one could use the same data {P_(r)(n),P_(t)(n−1)} totrain a single-tap adaptive equalizer. A properly designed equalizerwould be such that it coefficient tends to a value that could be takenas an approximation for

$\frac{1}{\alpha\left( {n + 1} \right)}.$

The structure of the algorithm is illustrated in FIG. 17, wherein the MSincludes a power adapter 1700, decoder 1702, and zero-order hold 1704,and the BS includes a power measurement block 1706, single-tap equalizer1708, selectable power control 1710, encoder 1712, decoder 1714, anddelay 1716. The channel between the BS and MS acts as a multiplier 1718between the signal transmitted by the MS and the channel power fadingφ(t).

In FIG. 17, the power measurement block measures the received powerP_(r)(n) averaged over a window duration of one power control period.The purpose of the single-tap equalizer is to estimate the inverse ofthe power channel. The equalizer could be a single-tap LMS(least-mean-square) filter. The tap ω_(E)(n) is adapted according to theruleω_(E)(n)=ω_(E)(n−1)+μu _(E)(n)(d _(E)(n)−u _(E)(n)ω_(E)(n−1))  (55)

where u_(E)(n)=P_(r)(n) and d_(E)(n)=P_(t)(n−1). With a proper choice ofthe step-size μ, and as time progresses, the adaptive filter tapapproximates

$\begin{matrix}{{\omega_{E}(n)} \approx \frac{1}{\phi\left( {n + 1} \right)}} & (56)\end{matrix}$

The tap of the equalizer, mimicking the inverse of the channel power, isused as the gain G. The transmission power is then estimated via{circumflex over (P)} _(t)(n)=GP _(d)  (57)

This information is coded to meet the power control bit rate requirementand transmitted to the MS. The same adaptive coding scheme used in theEC-CLPC algorithm can be used here. The mobile station will then decodethe transmission power information and use it as its transmission power.Since the BS knows what the transmission power is at each time, it willfeed it to the equalizer for online training.

The IE-CLPC algorithm is summarized in Table V below:

TABLE V Summary of the Inverse Estimation CLPC (IE-CLPC) algorithmInitialization: Choose the desired received power P_(d). Choose theequalizer's parameters: Filter order and μ. Choose a coder. For everypower control time sample n > 0 do: BS: 1. Measure P_(r)(n) from thereceived sequence. 2. Perform 1-tap equalization with input P_(r)(n) andreference P_(t)(n − 1). 3. Multiply the tap value by P_(d): [{circumflexover (P)}_(t)(n) = ω_(E)(n)P_(d)]. 4. Code {circumflex over (P)}_(t)(n).5. Send the coded data to the MS. MS: 6. Extract the coded data from thereceived data. 7. Decode the signal P_(t)(n). 8. Use P_(t)(n) directlyas the Tx power.

D. Algorithm 4: Optimal Predictive CLPC (OP-CLPC)

There are several other ways in which the transmitted power can beestimated, i.e., in which {circumflex over (P)}_(t)(n) can be computed.Apart from the schemes of FIGS. 14 and 17, we now discuss additionalmethods that follow by formulating the CLPC problem as aleast-mean-squares problem. Thus given a desired power level P_(d) and achannel attenuation factor φ, we consider the problem of determining thetransmitted power P_(t) that minimizes the mean-square error, i.e.,

$\begin{matrix}{\min\limits_{P_{t}}{E{{P_{d} - {\phi\; P_{t}}}}^{2}}} & (58)\end{matrix}$

A recursive (adaptive) solution for this problem can be expressed as{circumflex over (P)} _(t)(n−1)={circumflex over (P)}_(t)(n−2)+p(n)φ(n)e _(a)(n), n≧0  (59)where p(n) is the step-size sequence, say

$\begin{matrix}{{p(n)} = \frac{1}{\delta + {{\phi(n)}}^{2}}} & (60)\end{matrix}$for some small δ, ande _(a)(n)=P _(d)−φ(n){circumflex over (P)} _(t)(n−2).

Advancing time by one step, we get{circumflex over (P)} _(t)(n)={circumflex over (P)}_(t)(n−1)+p(n+1)φ(n+1)(P _(d)−φ(n+1){circumflex over (P)}_(t)(n−1))  (61)

Since p(n+1) and φ(n+1) are not available at time n, these twoquantities need to be estimated by predicting p(n) and φ(n) one stepahead. Therefore, the final expression for the transmission powerestimate is given by{circumflex over (P)} _(t)(n)={circumflex over (P)} _(t)(n−1)+p_(p)(n+1|n)φ_(p)(n+1|n)(P _(d)−φ_(p)(n+1|n){circumflex over (P)}_(t)(n−1))  (62)

where p_(p)(n+1|n) and φ_(p)(n+1|n) are one-step predictors of p(n) andφ(n), respectively.

FIG. 18 shows how the solution proposed by this algorithm can beimplemented. The BS includes a summing junction 1800, multiplier 1802,op-amp 1804, encoder 1806, power measurement block 1808, and ratio block

${\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi(n)}1810},$and the MS includes a decoder 1812, integrator 1814, zero-order hold1816, and selectable power control 1818. The channel between the BS andMS acts as a multiplier 1820 between the signal transmitted by the MSand the channel power fading φ(t).

We notice in this case that the ratio φ_(p)(n+1|n)/φ(n) is multiplied bythe received power P_(r)(n) since

$\begin{matrix}{{\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi_{n}}{P_{r}(n)}} = {{\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi(n)}{\phi(n)}{P_{t}\left( {n - 1} \right)}} = {{\phi_{p}\left( {{n + 1}❘n} \right)}{P_{t}\left( {n - 1} \right)}}}} & (63)\end{matrix}$

The OP-CLPC algorithm is summarized in Table VI below:

TABLE VI Summary of the Optimal Predictive CLPC (OP-CLPC) algorithmInitialization: Choose the desired received power P_(d). For NLMStopology, choose a small δ. Choose a coder. Choose the predictionparameters: Filter order, μ, and U. For every power control time samplen > 0 do: BS: 1. Measure P_(r)(n) from the received sequence. 2. KnowingP_(t)(n − 1), estimate φ(n). 3. Predict φ_(p)(n + 1|n). 4.${Multiply}\mspace{14mu}{P_{r}(n)}\mspace{14mu}{by}\mspace{14mu}{\frac{\phi_{p}\left( {{n + 1}❘n} \right)}{\phi(n)}.}$5. Compare the result with P_(d). 6. Multiply the difference by φ(n). 7.$\begin{matrix}{{{Multiply}\mspace{14mu}{the}\mspace{14mu}{result}\mspace{14mu}{by}\mspace{14mu}{the}\mspace{14mu}{step}\text{-}{size}\mspace{14mu}{p(n)}},} \\{\left\lbrack {{{\hat{P}}_{t}(n)} = {{\phi(n)}{p(n)}{e_{a}(n)}}} \right\rbrack.}\end{matrix}\quad$ 8. Code the signal {circumflex over (P)}_(t)(n). 9.Send the coded data to the MS. MS: 10.  Extract the coded data from thereceived data. 11.  Decode the signal P_(t)(n).

VII. Error Coding Power Control

Now we move to the third class of proposed methods for power control. Inconventional CLPC (see FIG. 3), only the sign of error is transmittedfrom the BS to the MS. We propose in this section a new algorithm, knownas Error Coding CLPC (EC-CLPC). This algorithm simply replaces the signblock in conventional CLPC by a more sophisticated encoding/decodingblocks. The purpose of this change is to send more information to the MSabout the error than just its sign. This makes the MSincrement/decrement its power by amounts proportional to the errorsignal amplitude.

FIG. 19 illustrates shows how the solution proposed by this algorithmcan be implemented. The BS includes a summing junction 1900, encoder1902, and power measurement block 1904, and the MS includes a decoder1906, integrator 1908, op-amp 1910, zero-order hold 1912, and poweradapter 1914. The channel between the BS and MS acts as a multiplier1916 between the signal transmitted by the MS and the channel powerfading φ(t).

The closed loop system shown in FIG. 19 looks similar to that of theconventional CLPC of FIG. 1. The new structure replaces the sign blockin FIG. 3 by a coding block. The purpose of this block is toencode/decode the value of the error signal e_(a)(n). The idea is toprovide the MS with more information of the error than just its signb(n).

The power error e_(a)(n) is coded at the BS using a generic sourcecoder. The output of the coder y(n) is transmitted to the MS. Nospecific coder will be addressed here and the performance of thisalgorithm will be dependent on the accuracy of the coder.

At the MS side, the signal y(n) is extracted and then decoded to get theerror estimate ê_(a)(n). This estimate is then passed through theintegration block to compute the transmission power, i.e.,P _(t)(n)=P _(t)(n−1)+ê _(a)(n)  (64)

The EC-CLPC algorithm is summarized in Table VII below.

TABLE VII Summary of the Error Coding CLPC (EC/CLPC) algorithmInitialization: Choose the desired received power P_(d). Choose a coder.Choose Tx gain A. For every power control time sample n > 0 do: BS: 1.Measure P_(r)(n) from the received sequence. 2. Compare P_(r)(n) toP_(d). 3. Code the difference signal e_(a)(n). 4. Send the coded signalto the MS. MS: 5. Decode the difference signal ê_(a)(n). 6. IncrementP_(t)(n) by ê_(a)(n).

VIII. Simulations

The algorithms developed in this work have been simulated. The followingare the simulation parameters used:

-   -   Desired power level P_(d) 0 dB.    -   Power bit rate: 1500 Hz.    -   Up-sampling factor (U): 2.    -   Channel:    -   Type: frequency selective multi-path Rayleigh fading.    -   Taps: 2.    -   Vehicle speed: variable.

The standard deviation of the power control error is used as a measureof how well the power control algorithms achieve the desired receivedpower. The exponent term α and the prediction step-size μ are chosen as1.3 and 0.8, respectively, unless otherwise specified. The standarddeviations of the PCE obtained from conventional CLPC for differentDoppler frequencies are shown in Table VIII for reference.

TABLE VIII Power control error STD obtained using conventional CLPCf_(D) Vehicle Speed PCE_(std) (Hz) (km/h) (dB) 10 6.7 0.5 20 13.3 0.7 5033.3 1.0 85 56.7 1.2 100  66.7 1.5 150  100 2.2

We start out tests by investigating the effect of μ and α on theperformance of the PR-CLPC algorithm. FIG. 20 shows the effect ofchoosing different μ on the PCE standard deviation for different valuesof f_(D). Choosing μ=0.85 results in best performance as indicated bythe vertical heavy arrow in the figure. This PCE can be further reduceddepending on the choice of the exponent term α as shown in FIG. 21. Theoptimal PCE changes in a nonlinear fashion with respect to α. When theDoppler frequency of the mobile unit can be measured, then we can referto FIG. 21 for the optimal choice of α. However, if the Dopplerfrequency cannot be measured accurately, then a choice of α=1.3 seems tobe reasonable as indicated by the vertical arrow in the figure.

The APR-CLPC algorithm is tested via simulations. FIG. 22 shows the STDof the PCE for two different values of the adaptation constant C. Thesaturation limits for α are chosen as α_(min)=1.1 and α_(max)=2.Increasing C will improve the performance of the CLPC algorithm at highvehicle speeds but will degrade it at low speeds. Choosing C=0.1 wasfound reasonable for all tested applications.

FIG. 23 shows a typical response of the adaptive coding term α_(c)(n),used in the ADI-CLPC algorithm as a function of time with f_(D)=85 Hz.The mean and variance values for α_(c)(n) in this example are 1.22 and0.02, respectively.

Finally, FIG. 24 shows PCE performance of the PR-CLPC, APR-CLPC,DI-CLPC, and ADI-CLPC. The coding parameters d(0) and α_(c) used in theDI-CLPC algorithm are chosen as 1E-3 and 1.8, respectively. Moreover,the parameters C, α_(min), α_(max) for the ADI-CLPC algorithm are set to0.1, 1.1, and 2, respectively. FIG. 24 includes also the performance ofthe conventional CLPC and that of an adaptive CLPC developed in [14],for the sake of comparison. The ADI-CLPC demonstrates the bestperformance over all other algorithms.

The IE-CLPC and OP-CLPC algorithms are also implemented usingsimulations. In simulating these algorithms, we assume that a coder isavailable which results in certain SNR, where the SNR of the coder isdefined as

${SNR} = \frac{\sigma_{x}^{2}}{\sigma_{e_{c}}^{2}}$

where x is the input to the encoder and e_(c) is the coding error (thedifference between the output of the decoder and x). In this experiment,we choose a value for the SNR and then measure the corresponding PCE. Werepeat this experiment for different SNR values.

In the IE-CLPC, a single-tap NLMS linear filter is used to perform theequalization with step-size μ=0.9. FIGS. 25 and 26 show the coding SNRversus PCE for f_(D)=[10, 20, 50, 85, 100, 150]Hz. The figures includealso the PCE error for conventional CLPC (heavy line) at these Dopplerfrequencies for th sake of comparison. To make improvement overconventional CLPC, it is necessary to have a coding SNR that is aboethis line. For example, at f_(D)=20 Hz, coding SNR should be more than14 dB for this algorithm to show improvement over conventional CLPC.

The same test is applied to the OP-CLPC algorithm. FIGS. 27 and 28 showthe SNR versus PCE plots for all f_(D) under study for the OP-CLPCalgorithm.

We apply this test again to the EC-CLPC algorithm. The coding SNR inthis case becomes

${SNR} = \frac{\sigma_{e_{a}}^{2}}{\sigma_{{\hat{e}}_{a} - e_{a}}^{2}}$

FIG. 29 shows the coding SNR required for a certain PCE for f_(D)=[10,20, 50]Hz. The same relation for f_(D)=[85, 100, 150]Hz is shown in FIG.30. From these two figures, we can see that this algorithm requires ahigh coding SNR at moderate Doppler frequencies (more than 40 dB). Thisbehavior is common to all simulations made. Therefore, this algorithmperforms moderately well at low and high Doppler frequencies while itshows bad performance at moderate frequencies. Furthermore, we candetermine from these figures the minimum achievable PCE. No matter howhigh the coding SNR is, no further improvement in the PCE is expectedbehind this minimal value. For example, the minimum achievable PCE bythe EC-CLPC algorithm for f_(D)=100 Hz is 1.45 dB.

Table IX shows the minimum coding SNR required for the EC-CLPC, IE-CLPC,and OP-CLPC algorithms so that they show improvement over conventionalCLPC.

TABLE IX Minimum coding SNR for the EC-CLPC, IE-CLPC and OP-CLPCSNR_(min) f_(D) Vehicle Speed (dB) (Hz) (km/h) EC-CLPC IE-CLPC OP-CLPC10 6.7 27 17 20 20 13.3 19 14 17 50 33.3 38 14 15 85 56.7 28 13 16 100 66.7 23 12 16 150  100 10 9 16

The IE-CLPC algorithm demonstrates the best performance among otheralgorithms in terms of the minimum SNR required to achieve the PCEcorresponding to the conventional CLPC. EC-CLPC is the worst from theprospective. Moreover, we show in Table X the minimum achievable PCE forthese algorithms.

TABLE X Minimum achievable PCE for the EC-CLPC, IE-CLPC and OP-CLPCPCE_(min) f_(D) Vehicle Speed (dB) (Hz) (km/h) EC-CLPC IE-CLPC OP-CLPC10 6.7 0.5 0.18 0.05 20 13.3 0.6 0.3 0.06 50 33.3 0.9 0.7 0.2 85 56.71.2 0.82 0.23 100  66.7 1.4 1.22 0.25 150  100 1.8 1.78 0.5

The OP-CLPC algorithm has the best performance in terms of the minimumreachable PCE. The OP-CLPC performs very well compared to other twoalgorithms especially at high vehicle speeds. Once again, EC-CLPCalgorithm shows worst performance in terms of the minimum achievablePCE.

IX. Contributions of this Work

In this work, the conventional CLPC scheme used in IS-95 CDMA wirelesssystems is analyzed. It is found that the conventional CLPC implements asimilar structure to that of the adaptation scheme used in a previouslydeveloped ADM (adaptive delta modulation). Our analysis shows that thepower control error is a function of two factors (see (25)):

1. The variation in the channel power fading.

2. The quantization noise of the sign function.

The work also includes a method for predicting the channel power fading.This method uses an adaptive algorithm to perform prediction. It alsoimproves the prediction by oversampling the received power signal.

We then described three classes of methods to decrease the power controlerror in closed loop power control. We described several algorithms toimplement these methods.

The first algorithm described in this work, namely, PR-CLPC, minimizespart of power control error expression (36) by introducing a ratio blockat the BS receiver. It was shown that the new error expression is afunction of a prediction error of the channel power fading and not onthe difference in fading samples as in conventional CLPC. Thus, anyprediction with acceptable accuracy will improve the power controlerror. The prediction method proposed in Section III is used here. Whencompared with conventional CLPC, the algorithm shows less power errorsfor all vehicle speeds tested.

The second algorithm is named APR-CLPC. This algorithm is similar toPR-CLPC except that the exponent term α is adapted to cope with largevariations in the channel fading. Simulations of this algorithm show animproved error performance over PR-CLPC.

In the DI-CLPC algorithm, the BS approximates the transmission powerthat should be used by MS. It then conveys this information to the MSthrough suitable source coding. This algorithm shows an improvedperformance over conventional CLPC, especially at higher vehicle speeds.

The DI-ClPC algorithm is extended to the adaptive case, where theexponent term α_(c) inside the coder is now adapted. The new algorithmis denoted ADI-CLPC. This algorithm shows the best performance among allproposed algorithms.

We also described two additional algorithms, namely, IE-CLPC andOP-CLPC. In the IE-CLPC, the BS estimates the inverse of the channelthrough equalization. It then transmits this information to the MS,which in turn uses it as its transmission power. In the OP-CLPC, thepower control problem is posed as a least-mean-squares optimizationproblem.

The last algorithm described in this work is named EC-CLPC. In thisalgorithm, the BS transmits more information about the power error tothe MS than just its sign. The MS then uses this extra information toimprove the performance of the loop.

The IE-CLPC, OP-CLPC, and EC-CLPC algorithms depend heavily on theperformance of the coding scheme used to convey information. Therefore,the simulations of these four algorithms are made in terms of theperformance of the coding scheme used. It was shown through simulationsthat these four algorithms can improve the performance of the CLPCprovided that a low-error coding scheme is used.

X. References

The following references are incorporated by reference herein:

[1] T. Ojanpera and R. Prasad, Wideband CDMA for Third Generation MobileCommunications, Artech House, London, 1998.

[2] W. Xinyu, G. Ling, and L. Guoping, “Adaptive power control on thereverse link for CDMA cellular system,” Proc. of APCC/OECC'99—5^(th)Asia Pacific Conference on Communications/4^(th) Optoelectronics andCommunications Conference, Beijing China, October 1999, vol. 1, pp.608-11.

[3] S. Nourizadeh, P. Taaghol and R. Tafazolli, “A Novel Closed LoopPower Control for UMTS,” First International Conference on 3G MobileCommunication Technologies, London, UK, March 2000, pp. 56-9.

[4] S. Park and H. Nam, “DS/CDMA closed-loop power control with adaptivealgorithm,” Electronics Letters, IEE, Aug. 19, 1999, Vol. 35, No. 17,pp. 1425-7.

[5] M. Sim, E. Gunawan, B. Soong and C. Soh, “Performance study ofclose-loop power control algorithms for a cellular CDMA system,” IEEETransactions on Vehicular Technology, IEEE, May 1999, Vol. 48, No. 3,pp. 911-21.

[6] H. Su and E. Geraniotis, “Adaptive closed-loop power control withquantized feedback and loop filtering,” Ninth IEEE InternationalSymposium on Personal, Indoor and Mobile Radio Communications, Boston,Mass., USA, September 1998, IEEE, Vol. 2, pp. 926-31.

[7] S. Choe, T. Chulajat, H. Kwon, K. Byung-Jin and S. Hong, “Linearprediction at base station for closed loop power control,” IEEE 49^(th)Vehicular Technology Conference, Houston, Tex., USA, May 1999, Vol. 2,pp. 1469-73.

[8] J. Tanskanen, A. Huang and I. Hartime, “Predictive power estimatorsin CDMA closed loop power control,” 48^(th) IEEE Vehicular TechnologyConference, Ottawa, Ont., Canada, May 18-21, 1998, IEEE, Vol. 2, pp.1091-5.

[9] A. Abrardo and D. Sennati, “On the analytical evaluation ofclosed-loop power-control error statistics in DS-CDMA cellular systems,”IEEE Trans. Vehic. Tech., Vol. 49, No. 6, pp. 2071-80, November 2000.

[10] F. Lau and W. Tam, “Intelligent closed-loop power control algorithmin CDMA mobile radio system,” Electronics Letters, Vol. 35, No. 10, pp.785-6, May 1999.

[11] M. Aldajani and A. H. Sayed, “An adaptive structure for sigma deltamodulation with improved dynamic range,” Proc. 43^(rd) Midwest Symposiumon Circuits and Systems, Lansing, Mich., August 2000.

[12] M. Aldajani and A. H. Sayed, “A stable adaptive structure for deltamodulation with improved performance,” Proc. ICASSP, vol. IV, Salt LakeCity, Utah, May 2001.

[13] M. Aldajani and A. H. Sayed, “Stability and performance analysis ofan adaptive sigma delta modulator,” IEEE Trans. Circuits and Sytems II,vol. 48, no. 3, pp. 233-244, March 2001.

[14] C. Lee and C. Steele, “Closed-loop power control in CDMA systems”Iee Proceedings-Communications, vol. 143, no. 4, pp. 231-9, August 1996.

[15] V. Garg and J. Wilkes, Principles and Applications of GSM, PrenticeHall, N.J., 1999.

XI. Conclusion

This concludes the description of the preferred embodiment of theinvention. The following describes some alternative embodiments foraccomplishing the present invention.

For example, any type of wireless communications system could be usedwith the present invention. Moreover, any type of base or mobile stationcould benefit from the present invention. Further, various commands orcodings could be used in place of those found in the preferredembodiments, without departing from the scope of the present invention.Finally, different sequences of steps, commands or functions or adaptivefilters could be used in place of those found in the preferredembodiments, without departing from the scope of the present invention.

In summary, the present invention analyzes a conventional closed loopcontrol (CLPC) and derives an expression for the power control error interms of the channel fading. The expression suggests methods forreducing the error variance. This is achieved by using a predictiontechnique for estimating the channel power fading via oversampling ofthe received and transmitted powers. The prediction module is thencombined with several proposed schemes for closed loop power control.The resulting architectures are shown to result in improved performancein extensive simulations.

The foregoing description of one or more embodiments of the inventionhas been presented for the purposes of illustration and description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed. Many modifications and variations are possiblein light of the above teaching. It is intended that the scope of theinvention be limited not by this detailed description, but rather by theclaims appended hereto.

1. A method of power control in a wireless communications system,comprising: (a) measuring a received power from a mobile station at abase station; (b) estimating a channel power fading from a previoustransmission power; (c) generating a predicted channel power fading; (d)multiplying the received power by a ratio of the predicted channel powerfading divided by the estimated channel power fading to generate aresult; (e) comparing the result with a desired power level to determinea power command for the mobile station; and (f) transmitting the powercommand to the mobile station, wherein the mobile station increments ordecrements its transmission power by a step change in response to thepower command.
 2. An apparatus for power control in a wirelesscommunications system, comprising: (a) means for measuring a receivedpower from a mobile station at a base station; (b) means for estimatinga channel power fading from a previous transmission power; (c) means forgenerating a predicted channel power fading; (d) means for multiplyingthe received power by a ratio of the predicted channel power fadingdivided by the estimated channel power fading to generate a result; (e)means for comparing the result with a desired power level to determine apower command for the mobile station; and (f) means for transmitting thepower command to the mobile station, wherein the mobile stationincrements or decrements its transmission power by a step change inresponse to the power command.
 3. A method of power control in awireless communications system, comprising: (a) measuring a receivedpower from a mobile station at a base station; (b) estimating a channelpower fading from a previous transmission power; (c) generating apredicted channel power fading; (d) multiplying the received power by aratio of the predicted channel power fading divided by the estimatedchannel power fading to generate a result; (e) comparing the result witha desired power level to determine a power command for the mobilestation; and (f) transmitting the power command to the mobile station,wherein the mobile station computes a signal from the power command andpreviously-received power commands, computes a term from the signal,computes a step change from the term and increments or decrements itstransmission power by the step change.
 4. The method of claim 3, furthercomprising: computing the term α(n) from:α(n)=α(n−1)+λ(n)C where C is a positive constant and λ(n) is the signalaccording to: ${\lambda(n)} = \left\{ \begin{matrix}{+ 1} & {{{if}\mspace{14mu}{b(n)}} = {{b\left( {n - 1} \right)} = {b\left( {n - 2} \right)}}} \\{- 1} & {{{if}\mspace{14mu}{b(n)}} \neq {b\left( {n - 1} \right)}} \\0 & {otherwise}\end{matrix} \right.$ b(n) is the power command, and b(n−1) and b(n−2)are the previously-received power commands, and the term α(n) is limitedby lower and upper bounds: ${\alpha(n)} = \left\{ \begin{matrix}\alpha_{\max} & {{{if}\mspace{14mu}{\alpha(n)}} > \alpha_{\max}} \\\alpha_{\max} & {{{if}\mspace{14mu}{\alpha(n)}} < \alpha_{\min.}}\end{matrix} \right.$
 5. The method of claim 3, further comprising:computing the step change ψ(n) according to:ψ(n)=10 log₁₀α(n).
 6. An apparatus for power control in a wirelesscommunications system, comprising: (a) means for measuring a receivedpower from a mobile station at a base station; (b) means for estimatinga channel power fading from a previous transmission power; (c) means forgenerating a predicted channel power fading; (d) means for multiplyingthe received power by a ratio of the predicted channel power fadingdivided by the estimated channel power fading to generate a result; (e)means for comparing the result with a desired power level to determine apower command for the mobile station; and (f) means for transmitting thepower command to the mobile station, wherein the mobile station computesa signal from the power command and previously-received power commands,computes a term from the signal, computes a step change from the termand increments or decrements its transmission power by the step change.7. The apparatus of claim 6, further comprising means for: computing theterm α(n) from:α(n)=α(n−1)+λ(n)C where C is a positive constant and λ(n) is the signalaccording to: $\lambda = \left\{ {\begin{matrix}\begin{matrix}{+ 1} \\{- 1}\end{matrix} \\0\end{matrix}\begin{matrix}\begin{matrix}{if} \\{if}\end{matrix} \\{\;{otherwise}}\end{matrix}\begin{matrix}\begin{matrix}{{b(n)} = {{b\left( {n - 1} \right)} = {b\left( {n - 2} \right)}}} \\{\;{{b(n)} \neq {b\left( {n - 1} \right)}}}\end{matrix} \\\;\end{matrix}} \right.$ b(n) is the power command, and b(n−1) and b(n−2)are the previously-received power commands, and the term α(n) is limitedby lower and upper bounds:$\alpha = {\left( \text{n} \right)\left\{ \begin{matrix}{{\alpha_{\max}\mspace{14mu}{if}\mspace{14mu}{\alpha(n)}} > \alpha_{\max}} \\{{\alpha_{\max}\mspace{14mu}{if}\mspace{14mu}{\alpha(n)}} < \alpha_{\min.}}\end{matrix} \right.}$
 8. The apparatus of claim 6, further comprisingmeans for: computing the step change ψ(n) according to:ψ(n)=10 log₁₀α(n).
 9. A method of power control in a wirelesscommunications system, comprising: (a) measuring a received power from amobile station at a base station; (b) estimating a channel power fadingfrom a previous transmission power; (c) generating a predicted channelpower fading; (d) generating an estimated transmission power from aratio of the desired power level divided by the predicted channel powerfading; (e) encoding the estimated transmission power to generateencoded data; and (f) transmitting the encoded data to the mobilestation, wherein the mobile station decodes the encoded data to obtainthe estimated transmission power and sets its transmission power to theestimated transmission power.
 10. An apparatus for power control in awireless communications system, comprising: (a) means for measuring areceived power from a mobile station at a base station; (b) means forestimating a channel power fading from a previous transmission power;(c) means for generating a predicted channel power fading; (d) means forgenerating an estimated transmission power from a ratio of the desiredpower level divided by the predicted channel power fading; (e) means forencoding the estimated transmission power to generate encoded data; and(f) means for transmitting the encoded data to the mobile station,wherein the mobile station decodes the encoded data to obtain theestimated transmission power and sets its transmission power to theestimated transmission power.
 11. A method of power control in awireless communications system, comprising: (a) measuring a receivedpower from a mobile station at a base station; (b) estimating a channelpower fading from a previous transmission power; (c) generating apredicted channel power fading; (d) generating an estimated transmissionpower from a ratio of the desired power level divided by the predictedchannel power fading; (e) encoding the estimated transmission power togenerate coded data; and (f) transmitting the coded data to the mobilestation, wherein the mobile station decodes the coded data to obtain theestimated transmission power and sets its transmission power to theestimated transmission power.
 12. An apparatus for power control in awireless communications system, comprising: (a) means for measuring areceived power from a mobile station at a base station; (b) means forestimating a channel power fading from a previous transmission power;(c) means for generating a predicted channel power fading; (d) means forgenerating an estimated transmission power from a ratio of the desiredpower level divided by the predicted channel power fading; (e) means forencoding the estimated transmission power to generate coded data; and(f) means for transmitting the coded data to the mobile station, whereinthe mobile station decodes the coded data to obtain the estimatedtransmission power and sets its transmission power to the estimatedtransmission power.
 13. A method of power control in a wirelesscommunications system, comprising: (a) measuring a received power from amobile station at a base station; (b) performing a 1-tap equalizationusing the measured received power as an input and a previoustransmission power as a reference; (c) multiplying a tap value from the1-tap equalization by a desired power level to generate an estimatedtransmission power; (d) encoding the estimated transmission power togenerate coded data; and (e) transmitting the coded data to the mobilestation, wherein the mobile station decodes the coded data to obtain theestimated transmission power and sets its transmission power to theestimated transmission power.
 14. An apparatus for power control in awireless communications system, comprising: (a) means for measuring areceived power from a mobile station at a base station; (b) means forperforming a 1-tap equalization using the measured received power as aninput and a previous transmission power as a reference; (c) means formultiplying a tap value from the 1-tap equalization by a desired powerlevel to generate an estimated transmission power; (d) means forencoding the estimated transmission power to generate coded data; and(e) means for transmitting the coded data to the mobile station, whereinthe mobile station decodes the coded data to obtain the estimatedtransmission power and sets its transmission power to the estimatedtransmission power.
 15. A method of power control in a wirelesscommunications system, comprising: (a) measuring a received power from amobile station at a base station; (b) estimating a channel power fadingfrom a previous transmission power; (c) generating a predicted channelpower fading; (d) multiplying the received power by a ratio of thepredicted channel power fading divided by the estimated channel powerfading to generate a first result; (e) comparing the first result with adesired power level to determine a difference; (f) multiplying thedifference by the estimated channel power fading to generate a secondresult; (g) multiplying the second result by a step size to generate anestimated transmission power; (h) encoding the estimated transmissionpower to generate coded data; and (i) transmitting the coded data to themobile station, wherein the mobile station decodes the coded data toobtain the estimated transmission power and sets its transmission powerto the estimated transmission power.
 16. An apparatus for power controlin a wireless communications system, comprising: (a) means for measuringa received power from a mobile station at a base station; (b) means forestimating a channel power fading from a previous transmission power;(c) means for generating a predicted channel power fading; (d) means formultiplying the received power by a ratio of the predicted channel powerfading divided by the estimated channel power fading to generate a firstresult; (e) means for comparing the first result with a desired powerlevel to determine a difference; (f) means for multiplying thedifference by the estimated channel power fading to generate a secondresult; (g) means for multiplying the second result by a step size togenerate an estimated transmission power; (h) means for encoding theestimated transmission power to generate coded data; and (i) means fortransmitting the coded data to the mobile station, wherein the mobilestation decodes the coded data to obtain the estimated transmissionpower and sets its transmission power to the estimated transmissionpower.